Question

If the radius of earth were to shrink by one percent and mass remains same, then acceleration due to gravity on the surface of the earth would

• A. Increase by 2%
• B. Decrease by 2%
• C. Increase by 1%
• D. Decrease by 1%

Answer 1

Answer: (B)

Decrease by 2%

$\text{Given - * Radius of earth shoinks by / ofo}$

$\begin{array}{c}\text{we Rnow that}\\ g=\frac{GMe}{R^2}-\left(i\right)\end{array}$ $\begin{array}{c}\text{Taking logarithm both Sides in eq- (1)}\\ \log \left(g\right)=-2\log \left(R\right)+\log (G\cdot Me)\end{array}$

$\begin{array}{c}\text{Since only}R\text{is changing hence rest}\\ \text{of the values are constant.}\end{array}$

$\begin{array}{c}\text{Now Differentiating both Sides -}\\ \frac{dg}{g}=-2\cdot \frac{dR}{R}\end{array}$

$\text{we have change in earth radius}=1\%=\frac{dR}{R}$

$\frac{dg}{g}=-2\%$

$\begin{array}{c}\text{Hence the acceleration due to grawity}\\ \text{decreases by}2\%\end{array}$